Further improvements to the ptychographical iterative engine

Maiden, Andrew; Johnson, Dwayne; Li, Peng

doi:10.1364/optica.4.000736

Cited by 347 publications

(215 citation statements)

References 34 publications

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“…As a result, both A ν A † ν and B g B † g are Hermitian symmetric and hence define orthogonal projections for any ν and g. By the asymptotic (1 + ) λ(1+ )+1/2 ∼ e λ +λ 2 /2 we have P (n) ∼ e −λ 2 /2 √ 2πλ = e −(n−λ) 2 /(2λ) √ 2πλ . (91) 31 Namely in the low noise limit the Poisson noise is equivalent to the Gaussian noise of the mean |Af | 2 and the variance equal to the intensity of the diffraction pattern. The overall SNR can be tuned by varying the signal energy Af 2 .…”

Section: Resultsmentioning

confidence: 99%

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Fixed Point Analysis of Douglas--Rachford Splitting for Ptychography and Phase Retrieval

Fannjiang¹,

Zhang²

2020

SIAM J. Imaging Sci.

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Douglas-Rachford Splitting (DRS) methods based on the proximal point algorithms for the Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase retrieval.Fixed point analysis shows that the DRS iterated sequences are always bounded explicitly in terms of the step size and that the fixed points are linearly stable if and only if the fixed points are regular solutions. This alleviates two major drawbacks of the classical Douglas-Rachford (CDR) algorithm: slow convergence when the feasibility problem is consistent and divergent behavior when the feasibility problem is inconsistent.Moreover, the fixed point analysis decisively leads to the selection of an optimal step size which in turn renders the Gaussian DRS method in a particularly simple form with no tuning parameter (Averaged Projection-Reflection). When applied to the challenging problem of blind ptychography, which seeks to recover both the object and the probe simultaneously, the DRS methods converge geometrically and globally when properly initialized.

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Section: Resultsmentioning

confidence: 99%

“…We see that the Gaussian-DRS outperforms the Poisson-DRS, especially when the Poisson RE becomes unstable for NSR ≥ 35%. As noted in [10,31,50] fast convergence (with the Poisson log-likelihood function) may introduce noisy artifacts and reduce reconstruction quality.…”

Section: Test Objectsmentioning

confidence: 99%

Fixed Point Analysis of Douglas--Rachford Splitting for Ptychography and Phase Retrieval

Fannjiang¹,

Zhang²

2020

SIAM J. Imaging Sci.

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“…The multi-slice ptychography reconstruction was conducted using 1000 iterations of the regularized ptychographic iterative engine (Maiden et al, 2017). The probe function propagated from the wavefront reconstructed from the single-slice dataset was used as the starting guess for the probe on the front slice.…”

Section: Resultsmentioning

confidence: 99%

“…The wavefront exiting the last slice carries the depth information of the entire sample and propagates to the detector plane. The recorded far-field diffraction pattern is used to update the wavefront exiting from the last slice, where the probe and the object functions are decoupled using conventional ptychographic algorithms (Maiden & Rodenburg, 2009;Maiden et al, 2017). The obtained probe function is then sequentially back-propagated to the previous slices, and updates the corresponding probe and object functions on each slice.…”

Section: Introductionmentioning

confidence: 99%

Resolving 500 nm axial separation by multi-slice X-ray ptychography

Huang

Yan

et al. 2019

Acta Cryst Sect A

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Multi-slice X-ray ptychography offers an approach to achieve images with a nanometre-scale resolution from samples with thicknesses larger than the depth of field of the imaging system by modeling a thick sample as a set of thin slices and accounting for the wavefront propagation effects within the specimen. Here, we present an experimental demonstration that resolves two layers of nanostructures separated by 500 nm along the axial direction, with sub-10 nm and sub-20 nm resolutions on two layers, respectively. Fluorescence maps are simultaneously measured in the multi-modality imaging scheme to assist in decoupling the mixture of low-spatial-frequency features across different slices. The enhanced axial sectioning capability using correlative signals obtained from multi-modality measurements demonstrates the great potential of the multi-slice ptychography method for investigating specimens with extended dimensions in 3D with high resolution.

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“…Among the diverse techniques one method seems to be particularly popular among practitioners. In the physics literature this method is known as the Ptychographic Interative Engine (PIE), and is regarded as a standard approach for image formation from ptychographic data within the physics community [7,8]. Mathematically this approach is an alternating projection method which goes back to the work of Gerchberg and Saxton [9] and Fienup [10].…”

Section: Introductionmentioning

confidence: 99%

A direct solver for the phase retrieval problem in ptychographic imaging

Sissouno

Boßmann

Filbir

et al. 2020

Mathematics and Computers in Simulation

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Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field diffraction patterns of the whole sample are then obtained. From a mathematical point of view those measurements are the squared modulus of the windowed Fourier transform of the sample. Thus, we have a phase retrieval problem for local Fourier measurements. A direct solver for this problem was introduced by Iwen, Viswanathan and Wang in 2016 and improved by Iwen, Preskitt, Saab and Viswanathan in 2018. Motivated by the applied perspective of ptychographic imaging, we present a generalization of this method and compare the different versions in numerical experiments. The new method proposed herein turns out to be more stable, particularly in the case of missing data.

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Further improvements to the ptychographical iterative engine

Cited by 347 publications

References 34 publications

Fixed Point Analysis of Douglas--Rachford Splitting for Ptychography and Phase Retrieval

Fixed Point Analysis of Douglas--Rachford Splitting for Ptychography and Phase Retrieval

Resolving 500 nm axial separation by multi-slice X-ray ptychography

A direct solver for the phase retrieval problem in ptychographic imaging

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